Finite Group DatabasebetaFinite Group Databasebeta| order | 26901 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C49×C61 ⋊ C9 |
| Sylow | C61 ⋊ C49⋊C9 |
| Sylow | C49 ⋊ C61⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #22582218 |
| commutator, hypocenter | C49×C61 | C9 |
| Frattini | C3×C7 | #13046197 |
| Fitting, cosocle | C3×C49×C61 | C3 |
| socle, prime radical | C3×C7×C61 | ΓL(1,𝔽8) |
| LCS | G ▷ C49×C61 | |
| UCS | C1 ◁ C3 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 26901 |
Polycyclic presentation:
3,7,61,3,7|a^3=d,b^7=e^4,b^a=b^4e,c^a=c^13,e^a=e^42997 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26901, 5);